<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">u</font>, <font color="Maroon" title="c5">u1</font>, <font color="Maroon" title="c6">v</font>, <font color="Maroon" title="c7">v1</font>, <font color="Maroon" title="c8">w</font>, <font color="Maroon" title="c9">w1</font>, <font color="Maroon" title="c10">u2</font>, <font color="Maroon" title="c11">v2</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>;<br/>





















<b>assume </b><a NAME="E1:54"/><i><font color="Green" title="E32">A1</font></i>: 
 <a href="analmetr.html#R1" title="ANALMETR:pred.1">Gen</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 ;<br/>

<b>assume </b><a NAME="E2:54"/><i><font color="Green" title="E33">A2</font></i>: 
( <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font>,<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c8">w</font>,<font color="Maroon" title="c9">w1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 ;<br/>

<a NAME="E3:54"/><b>then </b>
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>
 
<b>by </b><i><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/>
<a NAME="E4:54"/><b>then </b><i><font color="Green" title="E34">A3</font></i>: 
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>;<br/>
<a NAME="E5:54"/>
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font>
 
<b>by </b><i><a class="txt" href="analort.html#E2:54"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/>
<a NAME="E6:54"/><b>then </b><i><font color="Green" title="E35">A4</font></i>: 
<font color="Maroon" title="c6">v</font>,<font color="Maroon" title="c7">v1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">w1</font>
 
<b>by </b><i><a class="ref" href="analoaf.html#T21" title="ANALOAF:th.21">ANALOAF:21</a></i>;<br/>
<a NAME="E7:54"/><i><font color="Green" title="E36">A5</font></i>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>
 
<b>by </b><i><a class="txt" href="analort.html#E2:54"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:54_1"/><i><font color="Green" title="E37">A6</font></i>: 
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">w1</font> &amp; <font color="Maroon" title="c6">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">v1</font> )
 ;<br/><a NAME="E2:54_1"/><b>then </b><i><font color="Green" title="E38">A7</font></i>: 
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">w1</font>
 <b>by </b><i><a class="txt" href="analort.html#E1:54"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="analort.html#T6" target="_self" title="ANALORT:th.6">Th6</a></i>;<br/><a NAME="E3:54_1"/>
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c8">w</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c9">w1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a>  <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font>
 <b>by </b><i><a class="txt" href="analort.html#E4:54"><i><font color="Green" title="E34">A3</font></i></a>, <a class="txt" href="analort.html#E6:54"><i><font color="Green" title="E35">A4</font></i></a>, <a class="txt" href="analort.html#E1:54_1"><i><font color="Green" title="E37">A6</font></i></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></i>;<br/><a NAME="E4:54_1"/><b>then </b>
 <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">u</font>, <a href="analort.html#K2" title="ANALORT:func.2">Ortm</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c5">u1</font> <a href="analoaf.html#R1" title="ANALOAF:pred.1">//</a> <font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font>
 <b>by </b><i><a class="txt" href="analort.html#E7:54"><i><font color="Green" title="E36">A5</font></i></a>, <a class="txt" href="analort.html#E2:54_1"><i><font color="Green" title="E38">A7</font></i></a>, <a class="ref" href="analoaf.html#T20" title="ANALOAF:th.20">ANALOAF:20</a></i>;<br/><b>hence </b><a NAME="E5:54_1"/>
<font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="ref" href="analort.html#D4" target="_self" title="ANALORT:def.4">Def4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:54"/>
( <font color="Maroon" title="c8">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">w1</font> or <font color="Maroon" title="c6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v1</font> or <font color="Maroon" title="c4">u</font>,<font color="Maroon" title="c5">u1</font>,<font color="Maroon" title="c10">u2</font>,<font color="Maroon" title="c11">v2</font> <a href="analort.html#R2" title="ANALORT:pred.2">are_COrtm_wrt</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font> )
 ;<br/>


</div>
